For some positive integer $n$, we are given $n^2$ subsets of a ground set, where every element appears in at most $n$ sets. Any element appearing in exactly $n$ sets is called "maximum". We want to determine whether we can choose at most $n-1$ elements so that for any maximum element, at least on...

I have only heard of / seen Grobner bases in passing, but my understanding is that they are much like vector bases but for polynomials instead of linear systems. I know polynomials are used in CAD and graphics at the very least. Is there any particular reason why I haven't seen Grobner bases in a...